The electromechanical processes responsible for fine-tuning in the cochlea are still a matter of controversy. Using our recently developed mathematical model, it was shown that when motility and force generation of independently acting outer hair cells are assumed to be the source of activity, the low-pass filter property of isolated hair cells clearly limits the degree to which waveforms on the cochlear partition can be sharpened. This multi-degree of freedom model was used to determine the space-frequency characteristics of the putative cochlear amplifier that enables the model to reproduce experimentally-determined tuning characteristics, assuming only that outer hair cells are activated by the motion of the tectorial membrane and exert forces on both the reticular lamina and basilar membrane. It was found that outer hair cells must not only sense localized motions, but must also act synergistically to sense the local wavelength along the cochlear partition. This model of cochlear mechanics has been extended to include nonlinear effects induced by saturation of the cochlear amplifier. We are now able to compute compression of the cochlear input/output relation (basilar membrane velocity vs. input pressure at the stapes) and harmonic distortion of basilar membrane time waveforms along the cochlear partition for a pure tone input. It is anticipated that this new theory will be able to also increase understanding on a variety on nonlinear phenomena including the production of combination tones, two-tone suppression, and oto-acoustic emissions. We have extended the model to include coiling of the cochlear partition. Our theory predicts that coiling geometrically amplifies low frequency waves 10 dB compared to a straight cochlea having otherwise identical properties. Significant progress has been made in determining the radial structure of the traveling wave.